This study will be a prospective, single-institution, single-arm phase II study of Axitinib in patients with unresectable recurrent and metastatic head and neck squamous cell carcinoma. The subjects will be started on treatment with 5 mg of Axitinib twice a day continuously, with subsequent dose escalation to 7 mg and then 10 mg twice a day in the absence of grade 2 or worse toxicities. This will be followed by clinical and/or radiologic response assessment after 8 weeks and subsequently every 2 months until disease progression or intolerable toxicity.